Question

) (MATLAB) Assume a sampling rate of 100 Hz. Filter the signal given by x(t) = 1 + sin(0.125zt) + 0.5 sin(0.25mt) + 0.25 sin(0.5zt) + 0.125 sin(nt) by filters of progressively lower cutoff frequencies of 50, 5, 0.5, and 0.05 Hz

Answer 1

close all,
clear all,
clc,

Fs = 100;
t=0:(1/Fs):1;

x = 1 + sin(0.125 * pi * t) + 0.5*sin(0.25 * pi * t) + 0.25*sin(0.5 * pi * t) + 0.125*sin(pi * t);
subplot(4,1,1); plot(x); title('Original Signal, x = 1 + sin(0.125 * pi * t) + 0.5*sin(0.25 * pi * t) + 0.25*sin(0.5 * pi * t) + 0.125*sin(pi * t)');
grid on, ylim([-3,3]);

Order=2;

Fc = 5; Wn = Fc/(Fs/2);
b = fir1(Order,Wn,'low'); hd = dfilt.dffir(b);
y = filter(hd,x);
subplot(4,1,2); plot(y); grid on, ylim([-3,3]);
str = strcat('Filtered InputSignal, Fc = 5Hz'); title(str);

Fc = 0.5; Wn = Fc/(Fs/2);
b = fir1(Order,Wn,'low'); hd = dfilt.dffir(b);
y = filter(hd,x);
subplot(4,1,3); plot(y); grid on, ylim([-3,3]);
str = strcat('Filtered InputSignal, Fc = 0.5Hz'); title(str);

Fc = 0.05; Wn = Fc/(Fs/2);
b = fir1(Order,Wn,'low'); hd = dfilt.dffir(b);
y = filter(hd,x);
subplot(4,1,4); plot(y); grid on, ylim([-3,3]);
str = strcat('Filtered InputSignal, Fc = 0.05Hz'); title(str);

Ongin al Signal, x-1 + sinD 125° pi , t) + 0.5'sinD·25° pi , t) + 0.25% in(.5" pi *) + 0.125,sin(pi *) 20 120 40 60 80 100 Filtered inputsignal, Fc = 5Hz 20 60 80 100 120 Filtered InputSignal, Fc 0.5HMz 20 40 60 80 100 120 Filtered InputSignal, Fc 0.05Hz 20 60 100 120